Question

if you try to rent an apartment or buy a house, you find that real estate representatives establish apartment rents and house prices on the basis of square meter of heated floor space. The data in the table give the square meter and sales prices of eight houses randomly selected from those sold in a small city. 46 108 74 49 75 61 9740 X (mº) Y(ten thousand Yuan) 9.85 20.05 14.05 11.50 15.15 11.25 16.50 7.85 (1) Find the least squares regression line for these data. (2) Give an estimate for error's standard deviation o. (ô ) (3) Determine whether there is a significant linear relationship between the house prices and house areas listed in Table, Test at the 5% level of significance (Reference 10,025 (6) =2.4469,) ? (20 marks)

Answer 1

1)

Sum of X = 550

Sum of Y = 106.2

Mean X = 68.75

Mean Y = 13.275

Sum of squares (SS_X) = 4199.5

Sum of products (SP) = 657.45

Regression Equation = ŷ = a + bX

b = SP/SS_X = 657.45/4199.5 = 0.15655

a = M_Y - bM_X = 13.28 - (0.16*68.75) = 2.51189

ŷ = 2.51189 + 0.15655X

2)

By using given formula in part (2), The standard deviation σ = 0.9919

The estimate of error standard deviation b1 = 0.01531

3)

The value of test statistic is given by formula

Zil-1 7- ue = 1

= b1/Se(β1)

= 0.15655/0.01531

= 10.2353

The value is 10.2353

Since $t_o_b_s_e_r_v_e$ value is greater than t_cric , we reject the null hypothesis and conclude that there is significant positive relationship between house price and house area.